LETTERS
PUBLISHED ONLINE: 9 MAY 2016 | DOI: 10.1038/NPHYS3760
Crystal structure of the superconducting phase of
sulfur hydride
Mari Einaga1*†, Masafumi Sakata1, Takahiro Ishikawa1, Katsuya Shimizu1†, Mikhail I. Eremets2†,
Alexander P. Drozdov2, Ivan A. Troyan2, Naohisa Hirao3 and Yasuo Ohishi3
A superconducting critical temperature above 200 K has
recently been discovered in H2 S (or D2 S) under high hydrostatic
pressure1,2 . These measurements were interpreted in terms
of a decomposition of these materials into elemental sulfur
and a hydrogen-rich hydride that is responsible for the
superconductivity, although direct experimental evidence for
this mechanism has so far been lacking. Here we report the
crystal structure of the superconducting phase of hydrogen
sulfide (and deuterium sulfide) in the normal and superconducting states obtained by means of synchrotron X-ray
diffraction measurements, combined with electrical resistance
measurements at both room and low temperatures. We
find that the superconducting phase is mostly in good
agreement with the theoretically predicted body-centred
cubic (bcc) structure for H3 S3 . The presence of elemental
sulfur is also manifest in the X-ray diffraction patterns, thus
proving the decomposition mechanism of H2 S to H3 S + S
under pressure4–6 .
Recently, a very high Tc of 200 K has been discovered in the
hydrogen sulfide system1,2 . This work was initiated by the prediction
of a substantial superconductivity in H2 S (ref. 7), which in turn
arises from the idea that hydrogen-dominant metallic alloys might
be superconductors with high critical temperature, similar to pure
metallic hydrogen8 .
The superconducting transition was proved by the sharp drop
of the resistance to zero, a strong isotope effect in a study of
D2 S, a shift of the superconducting transition with magnetic
field, and finally by measuring the magnetic susceptibility and
magnetization. As a likely explanation, the authors1,2 suggested
that H2 S decomposes under pressure (with the assistance of
temperature) to pure sulfur and some sulfur hydride with a higher
content of hydrogen (such as SH4 or similar). At the same time,
a theoretical work appeared which considered a different starting
material (H2 S)2 H2 (stoichiometry H3 S) and found R3m and Im-3m
structures under pressure above 111 GPa and 180 GPa, respectively3 .
These structures and other stoichiometric compounds were further
carefully studied theoretically by different groups in numerous
works4,6,9–25 and Tc ∼ 200 K was consistently obtained for the Im-3m
structure. The calculated Tc , as well as its pressure dependence9 ,
are close to the experimental data1,2 . This suggests that the high
Tc observed in the experiments relates not to H2 S, but to the
H3 S in the Im-3m structure. Later calculations supported this idea:
H2 S is indeed unstable at high pressures and should decompose
to sulfur and higher hydrides, most likely to H3 S4,6,12 . The goal
of the present work is to check experimentally the structure of
the superconducting hydrogen sulfide and compare it with the
theoretically predicted structure.
Samples were prepared in the same way as described in refs 1,
2—H2 S was loaded at temperatures of ∼200 K, then the pressure
was increased to ∼150–170 GPa and the sample was annealed
at room temperature. Typical X-ray diffraction (XRD) images of
sulfur hydride and sulfur deuteride pressurized to 150–173 GPa are
shown in Fig. 1. The XRD patterns of sulfur hydride and sulfur
deuteride samples do not differ from each other. The diffraction
patterns seem to be produced by two major phases. This clearly
follows from the different pressure dependence of the peaks (Fig. 2
and Supplementary Fig. 3) and different variation of intensities
while scanning the sample over its diameter (Supplementary
Fig. 1): one group is fitted by elemental sulfur of the β-Po
structure26 and another group is described by the bcc structure
of H3 S from the theoretical work3 . We can conclude that H2 S
(D2 S) solid most likely decomposes under pressure via the route:
3H2 S → 2H3 S + S.
The pressure dependence of the atomic volume, Vatm , of sulfur
hydride and sulfur deuteride are shown in Fig. 2c. It is fitted
by a first-order Birch equation of state27 with the bulk modulus
B0 = 506 (30) GPa, and its pressure derivative B00 = 6 (fixed). The
value of the experimentally observed Vatm is slightly larger, but the
compressibility is in good agreement with Duan’s calculation3 . The
pressure dependence of the normalized atomic volume V /V0 of
elemental sulfur in the β-Po structure is shown in Supplementary
Fig. 3. It is in a good agreement with the experimental data of ref. 26
at high pressures P > 170 GPa, and with our density functional
theory calculations (see Methods).
Our powder XRD measurements do not allow us to distinguish
between the predicted bcc structures: Im-3m and R3m. In these
structures the positions of the sulfur atoms are the same and
the only difference is the position of the hydrogen atoms:
hydrogen atoms are situated symmetrically between neighbouring
sulfur atoms in the Im-3m structure and slightly asymmetrically
in the R3m structure (Supplementary Fig. 2). However, the
position of the hydrogen atoms cannot be determined from
the powder measurements, as hydrogen atoms are extremely
weak scatterers.
The low-temperature data help with further analysis. We
measured simultaneously the XRD and electrical resistance in
the same set-up28 (Fig. 3). The transition to the superconducting
state was determined from the sharp drop of the resistance
(Fig. 3a,b). We found that the normal and the superconducting
state have the same structure, as the XRD patterns are the same
1 KYOKUGEN,
Graduate School of Engineering Science, Osaka University, Machikaneyamacho 1-3, Toyonaka, Osaka 560-8531, Japan. 2 Max-Planck Institut
für Chemie, Hahn-Meitner-Weg 1, 55128 Mainz, Germany. 3 JASRI/SPring-8, 1-1-1, Sayo-cho, Sayo-gun, Hyogo 679-5198, Japan. † These authors
contributed equally to this work. *e-mail: [email protected]
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NATURE PHYSICS DOI: 10.1038/NPHYS3760
LETTERS
a
Intensity (a.u.)
b
λ = 0.41377 Å
Sulfur hydride
(150 GPa)
∗
∗
∗
bcc H3S (150 GPa)
β -Po sulfur (150 GPa)
10
15
20
25
2θ (°)
∗
d
λ = 0.41397 Å
Sulfur deuteride
(173 GPa)
∗
Intensity (a.u.)
Intensity (a.u.)
c
bcc H3S (170 GPa)
15
20
∗
∗
β -Po sulfur (170 GPa)
10
λ = 0.41290 Å
Sulfur deuteride
(173 GPa)
25
∗
∗
∗
300 K
∗
13 K
10
15
2θ (°)
20
25
2θ (°)
Figure 1 | XRD of the sulfur hydride and sulfur deuteride samples. a, Unrolled powder diffraction image of sulfur hydride at 150 GPa at room
temperature recorded on the imaging plate. b,c, Integrated XRD patterns obtained with subtraction of the background for sulfur hydride (b) and sulfur
deuteride (c). The patterns of bcc H3 S and β-Po elemental sulfur at 150 GPa and 170 GPa calculated according to refs 5,26 are shown beneath the
experimentally obtained patterns. Stars indicate peaks that do not belong to the sample, as follows from the scan over the sample (Supplementary Fig. 1):
these peaks remain unchanged, whereas the sample peaks change with the radius of the sample both in position and intensity. Open circles indicate a
reflection from the high-pressure phase IV of elemental sulfur (incommensurately modulated body-centred monoclinic structure). d, XRD patterns of
sulfur deuteride at 173 GPa at 300 K and 13 K. The peaks marked by stars are not reflections from the sample. The results of analyses are shown in
Supplementary Table 1.
λ = 0.41397 Å
∗
∗
103
∗
∗
111
∗
∗
123
10
Sulfur deuteride
c
∗
150 GPa
∗
15
20
This work
Sulfur hydride
Sulfur deuteride
EoS fit
Duan (2014) theory
R3m
Im-3m
25
180
∗
190
∗ ∗
133
∗
17
16
∗
∗ ∗
λ = 0.41397 Å
92
∗
∗
∗
b
∗
173 GPa
∗
10
Vatm (Å3)
Intensity (a.u.)
∗
Sulfur hydride
Intensity (a.u.)
a
15
20
25
2θ (°)
2θ (°)
15
14
13
12
100
150
200
250
Pressure (GPa)
Figure 2 | Pressure dependence of XRD in sulfur hydride and sulfur deuteride samples. a,b, XRD patterns taken at room temperature and different
pressures for sulfur hydride (a) and sulfur deuteride (b). Upper (red) and lower (green) ticks indicate the peak positions of the predicted bcc structure of
H3 S and β-Po elemental sulfur, respectively. The peaks marked with stars do not belong to the sample, as follows from Supplementary Fig. 1. On decreasing
the pressure in sulfur hydride, the phase transition of elemental sulfur is clearly observed—the peak from β-Po sulfur gradually disappears and that from
phase IV (open circle) is enhanced. c, Pressure dependence of the atomic volume of sulfur hydride and sulfur deuteride. The experimental data were
obtained with increasing pressure and are fitted with a first-order Birch equation of state (black solid line). The volumes of hexagonal (R3m) and bcc
(Im-3m) phases obtained from the theoretical work3 are shown as filled squares and filled triangles, respectively, connected with broken lines. The
estimated standard deviations are smaller than the size of the symbols.
at room and low temperatures (Fig. 1d). Moreover, the structure
of the sample does not change visibly over the pressure range
92–173 GPa. This is in a contrast to the dependence of the
critical temperature on pressure, which has a pronounced kink
at 150 GPa for H3 S and 160 GPa for D3 S (Fig. 3c). This kink
finds a natural explanation in the theoretical predictions9,23 : the
pressure dependence of the critical superconducting temperature
836
is different in the R3m phase at lower pressures and in the Im-3m
phase at higher pressures. Our XRD measurements support this
interpretation, as R3m and Im-3m phases differ only in the ordering
of the hydrogen atoms, and the same XRD patterns should be the
same in the both pressure domains. Thus, one can conclude that
the highest critical temperature of 203 K (ref. 2) corresponds to the
Im-3m phase.
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a 0.15
b
Sulfur hydride
LETTERS
0.05
c
Sulfur deuteride
133 GPa
0
50
100
150
200
250
0.03
190 GPa
0.02
173 GPa
150
100
0.01
150 GPa
300
Im-3m
200
Tc (K)
Resistance (Ω)
Resistance (Ω)
0.05
0.00
R3m
111 GPa
123 GPa
Sulfur hydride
Sulfur deuteride
250
0.04
0.10
300
0.00
50
0
50
Temperature (K)
100
150
200
250
300
Temperature (K)
0
100
150
200
250
Pressure (GPa)
Figure 3 | Pressure dependence of the superconducting transition in sulfur hydride and sulfur deuteride. a,b, Temperature dependence of resistance in
sulfur hydride (on decreasing pressure) (a) and sulfur deuteride (on increasing pressure) (b). c, Pressure dependence of critical temperature of
superconductivity Tc of sulfur hydride (black points) and sulfur deuteride (red points). Open circles and squares are taken from ref. 2. The points marked
with filled symbols are from the present work: the circles represent data on decreasing pressure, the squares and triangles on increasing pressure. Broken
lines (black for sulfur hydride and red for sulfur deuteride) indicate the phase boundary between the R3m and Im-3m structural phases. The error bars
indicate the difference between the onset temperature Tc and the zero-resistance temperature at each pressure in a and b.
Methods
Methods, including statements of data availability and any
associated accession codes and references, are available in the
online version of this paper.
Received 9 September 2015; accepted 12 April 2016;
published online 9 May 2016
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Acknowledgements
This work was performed under proposal No. 2015A0112 of the SPring-8. This
research was supported by Japan Society for the Promotion of Science Grant-in-Aid for
Specially Promoted Research, No. 26000006, JSPS KAKENHI, Grant-in-Aid for Young
Scientists (B), No.15K17707 and the European Research Council 2010-Advanced
Grant 267777.
Author contributions
M.E. took part in all the XRD measurements, data interpretation and writing the
manuscript. M.S. performed the cryogenic operations and XRD data collection. K.S.
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NATURE PHYSICS DOI: 10.1038/NPHYS3760
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performed in situ electrical resistance measurements in the XRD measurements and
writing the manuscript. T.I. performed support calculations for the data interpretation.
M.I.E. designed the study and participated in the XRD experiments and writing of the
manuscript. A.P.D. prepared the sample in a diamond anvil cell for all the experiments.
I.A.T. participated in building the Raman set-up. N.H. and Y.O. performed the
optimization of synchrotron XRD and cryogenic operations. M.E., K.S. and M.I.E.
contributed equally to this paper.
838
Additional information
Supplementary information is available in the online version of the paper. Reprints and
permissions information is available online at www.nature.com/reprints.
Correspondence and requests for materials should be addressed to M.E.
Competing financial interests
The authors declare no competing financial interests.
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NATURE PHYSICS DOI: 10.1038/NPHYS3760
Methods
The sample and electrical probes were prepared by similar method to ref. 2.
Angle-dispersive powder XRD measurements were carried out at SPring-8
(beamline BL10XU) with a monochromatic beam of energy ∼30.0 keV
(λ ∼ 0.412–0.414 Å). XRD and electrical resistance were measured simultaneously
with the aid of a cryostat28 . The diffraction patterns were recorded using an
imaging plate with an exposure time between 120 and 300 s. Four-probe electrical
measurements were performed with an a.c.-resistance bridge (Linear Research,
LR-700). We determined the pressure–volume dependence of β-Po sulfur by means
of first-principles calculations based on density functional theory. The Quantum
ESPRESSO code29 was used for the calculations, in which the
Perdew–Burke–Ernzerhof generalized gradient approximation30 and the Vanderbilt
ultrasoft pseudopotential31 were employed. The k-space integration over the
Brillouin zone was performed on a 24 × 24 × 24 grid, and the energy cutoff of the
plane wave basis was set at 80 Ry.
LETTERS
Data availability. Raw data were generated at the SPring-8 synchrotron
radiation facility (beamline BL10XU). Derived data supporting
the findings of this study are available from the corresponding author
on request.
References
29. Giannozzi, P. et al. QUANTUM ESPRESSO: a modular and open-source
software project for quantum simulations of materials. J. Phys. Condens. Matter
21, 395502 (2009).
30. Perdew, J. P., Burke, K. & Ernzerhof, M. Generalized gradient approximation
made simple. Phys. Rev. Lett. 77, 3865–3868 (1996).
31. Vanderbilt, D. Soft self-consistent pseudopotentials in a generalized eigenvalue
formalism. Phys. Rev. B 41, 7892–7895 (1990).
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